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Mathematics

THE EXACT HAUSDORFF MEASURE OF A GRAPH OF THE CAUCHY PROCESS ON THE LINE

Alfred Chukwumemeka Okoroafor

Alfred Chukwumemeka Okoroafor

Let Xt = {X(t),t0} be a Cauchy process on the line and for (0, 1), G(t) = {(X(t), t) : t [0, 1] } is a graph of X(t). We prove that 0 < – m(G(t)) < a.s., where (s) = s(log |log s|)|log s| and – m(E) is the -Hausdorff measure of E.

$70

8 Pages